Electron density—topological descriptors

Very similar to the electronic-topological descriptors, electron charge density connectivity index is defined for an - H-depleted molecular graph in which net atomic charges, calculated by computational chemistry, are used as weights for vertices [Estrada and Montero, 1993 Estrada, 1995d] ... 

L. F. Pacios, Topological descriptors of the electron density and the electron localization function in hydrogen bond dimers at short intermonomer distances, J. Phys. Chem. A 108, 1177-1188 (2004). 

For convenience, we shall classify the molecular models according to their topological dimensionality, p. A molecular conformation defined by the set of nuclear position vectors is a zero-dimensional (OD) model. A one-dimensional (ID) model corresponds to a molecular skeleton, defined by the set of nuclear positions and their connectivity (bond) matrix. Contour surfaces of one-particle molecular properties such as electron density or electrostatic potential are topologically two-dimensional (2D) models embedded in three dimensions. Finally, we find a true three-dimensional (3D) model whenever an entire one-electron property over all space is involved. This model can be regarded as the continuum of all 2D isoproperty surfaces. The difference among the models is summarized in Figure 1. We shall deal with pD models in this work (p = 0,1, 2, 3). Each of them requires a different type of shape descriptor. 

Descriptors used in the present study are calculated from the information about the connections between the atoms, from atomic 3-D coordinates, and from information about atomic electronic properties. In this work were used (i) graph theoretical (topological descriptors), (ii) geometric descriptors, (iii) electrostatic descriptors, (iv) 3-D descriptors for spectrum-like representation, and (v) density of states spectra. We elaborate on topological descriptors adopted in this particular work in view of a multitude of topological indices available and, in this way. 

However, when molecular descriptors are derived from molecular graphs, cis/trans isomerism is not usually recognized and some molecular descriptors were proposed in order to discriminate between cis/trans isomers, such as the - corrected electron charge density connectivity index, and - periphery codes. - Weighted matrices were also devised for obtaining the -> geometric modification number that is added to any topological index in order to discriminate cis/trans isomers. 

Since the topological charge density parameters are excellent descriptors of the electronic structure, it may be concluded that HOMA and NICS alike are associated with this characteristic of 7t and a electron systems, at least as far as benzenoid hydrocarbons are concerned. This result supports a view that there is an interplay between the ji and o electron structure. The charge density analysis shows that both structures contribute to the overall effect observed as aromaticity via indices as HOMA or NICS. 

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